Issues Removing Window Channel Balance
For the balance stuck in the up position, it may not be stuck at all; balances always have a constant upward tension so it's just behaving normally. It usually springs up because the top sash guide has broken, which is the part that keeps it in place. What you will need to do is lower it by hand until it's under the take out clip, then gently allow it to raise under it. The video below will go into more detail.
I'm less sure about the other side. That balance may in fact just be jammed. There's no trick to that, unfortunately. You could try soaking the track in WD-40 to see if that helps loosen it up some. That's always a safe and low-commitment option to try before anything else.